Question

X^2+(x+3)^2=225

Then what is the value of x

Answer 1

$\sf\ \: {x}^{2} + {(x + 3)}^{2} = 225 \\ \\ \sf\ \implies: {x}^{2} + {x}^{2} + 6x + 9 = 225 \\ \\ \sf\ \implies: {2x}^{2} + 6x + 9 - 225 = 0 \\ \\ \sf\ \implies: {2x}^{2} + 6x - 216 = 0 \\ \\ \sf\ \implies: 2( {x}^{2} + 3x - 108 ) = 0 \\ \\ \sf\ \implies: {x}^{2} + 3x - 108 = 0 \\ \\ \sf\ \implies: {x}^{2} + (12x - 9x) -1 08 = 0 \\ \\ \sf\ \implies: {x}^{2} + 12x - 9x - 108 = 0 \\ \\ \sf\ \implies:x(x + 12) - 9(x + 12) = 0 \\ \\ \sf\ \implies:(x - 9)(x + 12) = 0 \\ \\ \bf\ x - 9 = 0 \\ \sf\boxed{ \implies:x = 9 }\\ \\ \bf\ x + 12 = 0 \\ \sf\boxed{ \implies:x = - 12}$

Answer 2

$\bf\red{ \: {x}^{2} + {(x + 3)}^{2} = 225 }\\ \\ \bf\ \implies: {x}^{2} + {x}^{2} + 6x + 9 = 225 \\ \\ \sf\ \implies: {2x}^{2} + 6x + 9 - 225 = 0 \\ \\ \bf\ \implies: {2x}^{2} + 6x - 216 = 0 \\ \\ \bf\ \implies: 2( {x}^{2} + 3x - 108 ) = 0 \\ \\ \bf\ \implies: {x}^{2} + 3x - 108 = 0 \\ \\ \sf\ \implies: {x}^{2} + (12x - 9x) -1 08 = 0 \\ \\ \bf\ \implies: {x}^{2} + 12x - 9x - 108 = 0 \\ \\ \tt\ \implies:x(x + 12) - 9(x + 12) = 0 \\ \\ \bf\ \implies:(x - 9)(x + 12) = 0 \\ \\ \sf\ x - 9 = 0 \\ \bf\boxed{ \implies:x = 9 }\\ \\ \sf\ x + 12 = 0 \\ \bf\boxed{ \implies:x = - 12}$